An irregular parallelogram rotates 360° about the midpoint of its diagonal. how many times does the image of the parallelogram coincide with its preimage during the rotation? 2

Since parallelogram is irregular, its diagonals are not equal. Then the first time when the rotation image coincides with the preimage will be when the angle of rotation is equal to (then one half of diagonal lies on the another half of this diagonal) and the second time when the angle of rotation is equal to (when the image takes the initial position).